Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2005 ⋊ C2 |
| Sylow | C53 ⋊ #25198 |
958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1696 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(54,55)(56,60)(57,61)(58,63)(59,64)(62,74)(65,68)(66,75)(67,78)(69,76)(70,72)(71,79)(73,77)(80,83)(81,84)(82,85);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,57,59,73)(55,61,64,77)(56,66,69,82)(58,71,74,72)(60,75,76,85)(62,70,63,79)(65,80,78,84)(67,81,68,83);(54,56,58,68,59,69,74,67)(55,60,63,65,64,76,62,78)(57,66,72,81,73,82,71,83)(61,75,70,84,77,85,79,80);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55,58,63,59,64,74,62)(56,65,68,76,69,78,67,60)(57,70,72,77,73,79,71,61)(66,75,81,84,82,85,83,80)Polycyclic presentation:
2^8,53|a^2=f,b^2=f,c^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^52,c^b=cg,e^b=eh,g^b=gh,f^c=fh,i^c=i^52,e^d=eh,i^d=i^52716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 217694);